4 CONTENTS 1. Introduction Integration Indicators: Definitions and Properties Notation Degree of openness Degree of connection Degree of direct connection Degree of total connection Degree of integration Global indicators On the Evolution of International Economic Integration: Empirical Evidence Statistical sources and selected variables Degree of openness Degree of connection Degree of integration How do the different indicators relate? Integration Indicators: Relevance of Results Conclusions: Is Globalization Advancing? Appendix References About the Authors

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6 1. Introduction INTERNATIONAL economic integration (IEI) indicators can be classified into two broad categories, namely, those focusing on prices and those focusing on quantities. Other indirect approaches also take into account the importance of barriers to integration. However, these are not true indicators of international economic integration, but explanatory variables for their limits, i.e., explanatory variables for home-country bias, or for other biases such as geographical and flow-orientation biases. Some examples of this type of barrier thoroughly analyzed in the literature relate to distance and other nature-related hindrances, language, colonial, military or political relations, currencies, or trade agreements on trade tariffs (Brahmbhatt, 1998; Frankel, 2000; Knetter and Slaughter, 1999). Measures of integration based on prices are preferred by many scholars to consider an axiomatic criterion, i.e., the compliance with the law of one price (LOP), in different geographical markets. The assumption of the LOP enables us to measure ability for integration by eliminating price differentials for commodities and assets in different territories in perfectly competitive markets. However, a unique price would only exist for homogeneous goods, yet not for others that can be differentiated. Since imperfect competition is now at the core of the new theories of international trade (Krugman and Obstfeld, 2002), and differentiated commodities account for two thirds of world trade (Rauch, 1999), a set of criteria is required to establish international economic integration measures under conditions of imperfect competition. To date, this type of measure is unavailable 1, and therefore international economic integration indicators based on prices turn out to be misleading, and present difficulties if they are intended to be used as a general measure of the degree of international economic integration. In fact, several empirical studies that attempt to measure how far we are from complying with the rule based on the (LOP) include integration objectives that have not necessarily been attained. 1. Econometric estimations on the ability to explain deviations from the LOP are manifold (Knetter and Slaughter, 1999), yet they do not solve the key problem: the lack of a benchmark to measure integration that does not depend on perfect competition. 5

7 iván arribas fernández, francisco pérez garcía and emili tortosa-ausina The most commonly used integration measure based on quantities is the degree of openness defined as exports plus imports divided by GDP (XM/GDP). While it provides a straightforward approach, it is not free from disadvantages. The first of these although easily overcome is its traditional disregard for differing sizes of economies, in spite of the fact that a large country such as the U.S. devotes higher shares of its output to satisfying internal demand than a small country such as the Netherlands, since the former s share of world demand is much higher. Other limitations of the degree of openness become stricter when the number and importance of the trade connections each country has with the rest of the world are relevant aspects of integration, since the openness indicator completely disregards this issue. Indeed, the architecture of the network of world trade flows turns out to be very important when assessing integration from a globalization perspective, since some of its more relevant features are the multiplicity of flows (trade flows, capital flows, and human flows) in many directions, the adherence to the process of all countries, and the establishment of many other connection paths both direct and indirect, and physical or virtual between agents and economies. If these aspects are to be detected, international economic indicators must be given a higher degree of complexity. Nowadays the world economy is regarded as a field in which the progress of globalization plays a major part. According to the process of globalization introduced in the sixties by communications theorists such as Marshall McLuhan technology alters both social and economic ties, turning the world into a village in which national spaces are partly abolished, and individuals must learn to live in close relation to formerly distant agents. Any attempt to analyze economic integration in these circumstances must uncover what occurs when borders vanish, and the connections among individuals and economies proliferate. When measuring globalization we must identify the type of international economic integration that would be attained in a true world village, and calculate how far we are from that scenario. There is a remarkable consensus on what the main drivers of this process are. However, to date no consensus has been reached on the level of globalization attained, or its effects. Accordingly, many scholars share the opinion that the main drivers of international economic integration in the private sphere are technological change and the decline in transportation and communication costs, whereas in the public sphere they are associated with the gradual removal of political barriers to trade and investment and capital and human flows (Frankel and Rose, 2000). In turn, debate contin- 6

8 measuring international economic integration: theory and evidence of globalization ues on the consequences of globalization, its effects on growth and income distribution, as well as the changes to brings to competitiveness in firms and countries, the intensity of crises, or the governability of the international financial system (Rodrik, 1998 a, 1998 b; Salvatore, 2004; Bhagwati, 2004 a, 2004 b; Stiglitz, 2002). One of the main difficulties in obtaining conclusive empirical evidence on the consequences of globalization is the shortage of convincing measures. In recent years, some aspiring indicators of globalization have been developed, which take into account economic, political, technological and personal dimensions, aggregating several variables following ad hoc (nonparametric) and statistical (parametric, based on principal components or factor analysis) criteria (Dreher, 2005; Heshmati, 2006). Constructing this type of indicators consists simply of mixing up different traditional openness indicators (both on international trade and financial flows), yet letting unsolved the aforementioned difficulties. The validity of these indicators is justified by its ability to (statistically) explain certain international economic differences (especially on growth), yet it does not imply they apprehend the nature of the globalization process. The main aim of our study is to introduce measures for international economic integration and globalization starting from a set of basic axioms and the definition of a set of indicators conceived to achieve two objectives: to uncover the role of the network and to define a Standard of Perfect International Integration. 1) Uncovering the role of the network implies accepting that the advance of international economic integration operates through both higher openness and higher connectedness to other economies, following both direct and indirect paths. The latest wave of technological change and the removal of a series of barriers to international trade has boosted openness, but at the same time has produced a secondary effect, namely, economic agents in different parts of the world now have more links, through both direct and indirect paths. This increased number of connections may be efficient because of the development of information technology and the dramatic fall in transaction costs. Measuring international economic integration in the age of globalization must take into account that connections thrive by different means. When indirect relations are accounted for, we are able to verify whether the attained level of integration is higher than what other traditional openness and direct connection indicators might only suggest. At this point, it is perti- 7

9 iván arribas fernández, francisco pérez garcía and emili tortosa-ausina nent to ask how important the two components namely, increased openness and increased connectedness are to the progress of international economic integration. The available statistical information does not allow us to give a precise answer because of the lack of accurate data on indirect links between countries. However, some trends-such as the development of e-commerce networks, or the increasing policy of outsourcing stages in the production process, representing a breakdown in the vertically-integrated mode of production (Feenstra, 1998; Feenstra and Hanson, 1996, 1997, 1999) suggest that indirect connections are important and can contribute to the acceleration of the globalization process, thanks to the reduction in transport and transaction costs and greater reliance on international markets as a mechanism of resource allocation (Coase, 1937; Williamson, 1975; Grossman and Helpman, 2002, 2005). 2) Any attempt to characterize a scenario in which economies are entirely integrated/globalized (Standard of Perfect International Integration) is to describe the conditions under which the world economy would operate as a global village. This approach allows us to assess the distance that separates the current level of international economic integration from the scenario of complete globalization. In that ideal situation, not yet attained, both borders and distances (of whatever kind) are irrelevant. This situation not only requires countries to be more open, but also a full and unbiased development of the network of connections that link economies. A further step would be to measure biases in both directions (through the domestic economy or by prioritizing some connections over others), which would help to identify the factors that hinder the advance of globalization. While some of these obstacles may always be with us, others that might previously have been considered unmovable have now been eliminated by technical and/or technological progress. To achieve these two objectives, and to uncover the structure of the trade network that economies forge, we can contemplate the relations, or flows between them as the vectors of a graph in which the nodes represent the countries, and then analyze the degree of connectedness in the network using network analysis techniques 2. Although these techniques are some- 2. See, for instance, Carrington, Scott and Wasserman (2005), Wasserman and Faust (1992), Hanneman and Riddle (2005), among many others. 8

10 measuring international economic integration: theory and evidence of globalization what underused by economists, especially in comparison with other social sciences (Rauch, 2001), this approach is not new in international economics, and has attracted recent interest. In particular, several studies highlight the importance of information flowing through cultural, political or economic ties in order to explain both the intensity and the evolution of economic relations between countries (Rauch, 1999, 2001; Rauch and Trindade, 2002; Rauch and Casella, 2003; Greaney, 2003; Pandey and Whalley, 2004; Combes, Lafourcade and Mayer, 2005). Other works suggest applying formal network analysis concepts and instruments developed in other social sciences such as sociology to the study of the structure and dynamics of international trade 3. Smith and White (1992) rearrange old ideas such as blocks, center and periphery, that are relatively popular in debates on the evolution of world economy. Kali and Reyes (2005, 2007) transpose several concepts of network analysis (centrality, network, density, clustering, assortative mixing, maximum flow) to international economic integration. To analyze integration from the perspective outlined above, the main contents of the article are structured into two sections, one theoretical and the other empirical. The theoretical section (section 2) sets out the methodological contents of our approach to measure international economic integration. First, it takes a series of axioms to establish the approach and then uses them to define openness, connectedness and integration indicators together with their properties, and the Standard of Perfect International Integration. Section 3 contains the empirical application by considering data on exports of goods for a set of countries which account for virtually all world output, and for a relatively long sample period ( ). Section 4 presents evidence on the power of our indicators as explanatory variables for some traditional competitiveness indicators. Once the most important features of the globalization process have been analyzed from the results obtained, section 5 concludes. 3. International trade is not the only case. Other recent examples of network analysis applications can be seen in the field of labor economics (Calvó-Armengol and Jackson, 2004; Calvó-Armengol, 2004; Calvó-Armengol and Zenou, 2005), growth (Pérez et al., 2006), or bank efficiency (Pastor and Tortosa-Ausina, 2006). 9

11 2. Integration Indicators: Definitions and Properties THE international integration process starts with the openness of economies, but its effects and scope also depend on the structure of current relations between these economies. Relevant aspects of this structure include the number of economies each one is in contact with; whether the relationships are direct or indirect; the number of flows between them and the proportionality of these flows to the size of the economies 4. When producers exist in the global village, the level of integration is such that there is no difference in intensity (bias) that reinforces the exchanges inside the countries or from one specific economy to other. In other words, the economies, represented by countries, are not relevant except for their relative size, and they do not imply differences in trading time costs. To analyze the evolution of integration from this perspective we start with the following axioms on global village economies that must be verified by an integration index: Axiom 1. Openness. The more open an economy is, the more integrated it will be. Axiom 2. Balanced relationships. An economy that balances its direct relationships with other economies, in proportion to their size, will have a higher level of integration. Axiom 3. Indirect relationships. An economy that reinforces its relationships with other economies through indirect relationships across third economies will have a higher level of integration. 4. This approach has several links with the literature on social networks. See, for instance, Annen (2003), Hanneman and Riddle (2005), Karlin and Taylor (1975), Wasserman and Faust (1992), or Wellman and Berkovitz (1988). 10

12 measuring international economic integration: theory and evidence of globalization Axiom 4. Size. The bigger an economy is, the more relevant its integration will be for the world economy globalization (global level of integration). To determine the degree of integration we proceed in four stages, each one of which defines different indicators: 1. In the first stage we characterize the degree of openness. We start with the usual definition found in the literature but corrected for domestic bias to take into account the different sizes of the economies compared. 2. In the second stage we analyze whether the connection of one economy with others is proportional to their sizes in terms of GDP (gross deep product) 5, or whether this connection shows geographical bias which moves the situation away from that corresponding to a perfectly integrated world. Thus, we define the degree of direct connection to measure the discrepancy between the trade volumes in the real world and trade volumes corresponding to a perfectly integrated world. 3. Indirect relations between economies and the importance of these relations are considered in the third stage. To extend the analysis of economic integration in this direction we define the degree of total connection, which evaluates the importance of all direct and indirect relationships that economies establish with each other. 4. From the above concepts, we define the degree of integration. This combines degrees of openness and total connection, provided that both set limits to the integration level achieved. We show that the degree of integration verifies the four axioms presented above. The analysis of the four indicators is conducted on two levels, namely, the individual level, which focuses on each economy, and the global level, which corresponds to the analysis of all economies. In the second level the weight of each economy enters the aggregation analysis. 5. The dependence of exchanges on economy size is the focus of international trade analyses based on gravity models and widely used in the literature (Hummels and Levinsohn, 1995; Feenstra, Markusen and Rose, 1998; Feenstra, Markusen and Rose, 2001; Rauch, 1999). 11

13 iván arribas fernández, francisco pérez garcía and emili tortosa-ausina 2.1. Notation The geometry defined by the relationships among economies can be modeled as a network, where countries are nodes and there exists a vertix between two of them, say i and j, if there exists a flow from i to j. Thus, flow not only defines links among countries but also measures the intensity of the relationships. Thus, given a specific flow (for example, an export flow), we have the network associated to a global village economy, which is an ideal network and the network associated to reality. Our integration index is a measure of the distance between these two networks, the ideal one and the real one. Let N = {1,..., g} be the set of nodes or economies and let i and j be typical members of this set. Let g be the number of elements in N, i.e., the number of countries in the analyses. Let Y i be the size (activity volume) of economy i N, for example its GDP. We define a i as the economy i s relative weight with respect to the world economy, i.e., a i = Y i / S j N Y j. Given a measurable relationship among countries we define the flow X ij as the intensity of this relationship from economy i to economy j, for all i, j N. The flow among economies can be evaluated through either the imports or the exports of goods or capital, and in general it can be evaluated through any other flow measured in the same units as Y i. Moreover, in general the flow between two economies will be asymmetric, so that X ij will not necessarily be equal to X ji, for all i, j N. We also assume that X ii = 0 for all economy i N. All definitions in this paper depends on the flow considered to measure the international integration. If the orientation of production towards domestic demand is not biased, then its volume will not be the same in each economy since it depends on its size. In order to remove domestic bias we define Ŷ i as the production destined for export taking into account the weight in the world economy of the economy considered: Ŷ i = Y i a i Y i Degree of openness We define the relative flow or degree of openness between economies i and j as DO ij = X ij / Ŷ i. Given that X ii = 0, it follows that DO ii = 0 for all i N. Definition 1. Given an economy i N, we define its degree of openness, DO i, as 12

14 measuring international economic integration: theory and evidence of globalization DO i = SDO ij = j N S j N X ij. (2.1) By definition the above expression verifies Axiom 1. Degree of openness yields results (in general) within the interval [0, 1], where a value of 0 indicates that the economy is closed (compared to the measure of flow chosen) and a value of 1 indicates a lack of domestic bias in the economy (total openness). Although the degree of openness in an economy is, in general, lower than 1, some particular economies may exceed this value. DO is a relative indicator that takes into account economy size: domestic bias has been corrected, removing the effect of the size of economy i on DO. Differences in DO among economies can be attributable to different obstacles to integration (transport costs, political factors, etc.), one of which is scale, but differences cannot be due to bias in the measure of openness 6. Ŷ i 2.3. Degree of connection In the economic network, the relative flow from economy i to economy j in terms of the total flow of economy i, a ij, is given by a ij = X ij (2.2) S j N X ij (recall that we are assuming X ii = 0). Let A = (a ij ) be the square matrix of relative flows: the component ij of matrix A is a ij. We consider that an economic network (the world economy) is perfectly connected if the flow between two economies is proportional to their relative weights. An economy that is part of a perfectly connected network will emit flows to all other economies which must be proportional to the size of the recipient economy. Definition 2. A world economy is perfectly connected if the flow from economy i to economy j is equal to b ij Ŷ i where 6. We write DO instead of DO i when general statements on the degree of openness are being made, or references to the variable itself, which do not hang on any specific country. The same rule will be applied to the other indicators. 13

15 iván arribas fernández, francisco pérez garcía and emili tortosa-ausina Y j b ij =, (2.3) S Y k k N \ i is the relative weight of economy j in a world where economy i is not considered. Note that S j N/i b ij = 1 and that b ij is the degree of openness between economies i and j in the perfectly connected world, with b ii = 0. Let B = (b ij ) be square matrix of degrees of openness in the perfectly connected world, where the component ij of B is b ij. Remark 1. By definition we verify that S j N a ij = S j N b ij = 1, thus both matrixes A and B define Markov chains and it can be proved that they are recurrent irreducible aperiodic Markov chains Degree of direct connection Starting from the previously defined matrices, we can define the indicators that measure the distance between the real distribution of flows and those that correspond to a perfectly connected world. One of these indicators is the cosine of the angle of the vector of relative flows with the vector of the flows in a perfectly connected world. Definition 3. Given an economy i N we define the degree of direct connection of i, DDC i, as DDC i = S a ij b ij j N. (2.4) S(b ij) 2 j N S(a ij) 2 j N Although the cosine of two vectors oscillates between 1 and 1, the degree of direct connections always takes nonnegative values given that both vectors have only nonnegative components. DDC verifies Axiom 2 and provides a single number that should be close to 1 if the economy i is perfectly connected, and close to zero for an economy i whose flows are directed towards the smallest world economies Degree of total connection Both the real world matrix A and the perfectly connected world matrix B consider direct relative flows between economies. However, part of the 14

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